This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Welcome back Lïský — missed you this week. Step 1: Recall the formula for the distance covered in the n-th second. The distance S_n covered by an object in the n-th second of its motion, starting with initial velocity u and moving with uniform acceleration a, is given by: S_n = u + (a)/(2)(2n - 1) Step 2: Set up equations using the given information. For the 4th second, n=4 and S_4 = 5.5 m: 5.5 = u + (a)/(2)(2 × 4 - 1) 5.5 = u + (a)/(2)(8 - 1) 5.5 = u + (7a)/(2) (Equation 1) For the 8th second, n=8 and S_8 = 9.5 m: 9.5 = u + (a)/(2)(2 × 8 - 1) 9.5 = u + (a)/(2)(16 - 1) 9.5 = u + (15a)/(2) (Equation 2) Step 3: Solve the system of equations for acceleration a. Subtract Equation 1 from Equation 2: (u + (15a)/(2)) - (u + (7a)/(2)) = 9.5 - 5.5 (15a)/(2) - (7a)/(2) = 4.0 (8a)/(2) = 4.0 4a = 4.0 a = (4.0)/(4) a = 1.0\, m/s^2 Step 4: Substitute the value of a into Equation 1 to find the initial velocity u. 5.5 = u + (7(1.0))/(2) 5.5 = u + (7)/(2) 5.5 = u + 3.5 u = 5.5 - 3.5 u = 2.0\, m/s The acceleration of the car is 1.0 m/s^2 and its initial velocity is 2.0 m/s. Send me the next one 📸